Analysis of Instability and Self-Excited Vibration for Collapsible Tube by Distributed Parameter Model

Abstract The stability of a Starling resistor type collapsible tube circuit are studied on the basis of a distributed parameter model including no effect of flow separation at the collapsed part of the tube. The governing equations are spatially discretized into 200 sections and rearranged to 401 ordinary differential equations with respect to time. The stability of the circuit is examined by the characteristic equation of linearized governing equations. Transition of the stability according to variation of the flow rate is indicated as a root locus of the eigenvalues. The original nonlinear equations are numerically solved by Runge-Kutta scheme and the theoretical frequency and the amplitude of self-excited vibrations are compared with experimental results.